Covering action on Conley index theory

Autor(es)

Lima, D. V. S. ; Da Silveira, M. R. ; Vieira, E. R.

• Tipo de documento: Artigo Científico
• Fonte: Ergodic Theory and Dynamical Systems; v. N/A, p. 33-pg., 2022-02-21.

Resumo

In this paper we apply Conley index theory in a covering space of an invariant set S, possibly not isolated, in order to describe the dynamics in S. More specifically, we consider the action of the covering translation group in order to define a topological separation of S which distinguishes the connections between the Morse sets within a Morse decomposition of S. The theory developed herein generalizes the classical connection matrix theory, since one obtains enriched information on the connection maps for non-isolated invariant sets, as well as for isolated invariant sets. Moreover, in the case of an infinite cyclic covering induced by a circle-valued Morse function, one proves that the Novikov differential of f is a particular case of the p-connection matrix defined herein. (AU)

• Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 20/11326-8 - Uma abordagem algébrica-topológica para sistemas dinâmicos e topologia simplética
• Beneficiário: Dahisy Valadão de Souza Lima
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático